24,720 research outputs found
Representations of algebras as universal localizations
Every finitely presented algebra S is shown to be Morita equivalent to the
universal localization \sigma^{-1}R of a finite dimensional algebra R. The
construction provides many examples of universal localizations which are not
stably flat, i.e. Tor^R_i(\sigma^{-1}R,\sigma^{-1}R) is non-zero for some i>0.
It is also shown that there is no algorithm to determine if two Malcolmson
normal forms represent the same element of \sigma^{-1}R.Comment: v2 (minor revision of v1). 15 pages, LATEX, to be published in the
Mathematical Proceedings of the Cambridge Philosophical Societ
SIR epidemics with long range infection in one dimension
We study epidemic processes with immunization on very large 1-dimensional
lattices, where at least some of the infections are non-local, with rates
decaying as power laws p(x) ~ x^{-sigma-1} for large distances x. When starting
with a single infected site, the cluster of infected sites stays always bounded
if (and dies with probability 1, of its size is allowed to
fluctuate down to zero), but the process can lead to an infinite epidemic for
sigma <1. For sigma <0 the behavior is essentially of mean field type, but for
0 < sigma <= 1 the behavior is non-trivial, both for the critical and for
supercritical cases. For critical epidemics we confirm a previous prediction
that the critical exponents controlling the correlation time and the
correlation length are simply related to each other, and we verify detailed
field theoretic predictions for sigma --> 1/3. For sigma = 1 we find generic
power laws with continuously varying exponents even in the supercritical case,
and confirm in detail the predicted Kosterlitz-Thouless nature of the
transition. Finally, the mass N(t) of supercritical clusters seems to grow for
0 < sigma < 1 like a stretched exponential. The latter implies that networks
embedded in 1-d space with power-behaved link distributions have infinite
intrinsic dimension (based on the graph distance), but are not small world.Comment: 16 pages, including 28 figures; minor changes from version v
Noncommutative localization in algebraic -theory
Given a noncommutative (Cohn) localization which is
injective and stably flat we obtain a lifting theorem for induced f.g.
projective -module chain complexes and localization exact
sequences in algebraic -theory, matching the algebraic -theory
localization exact sequence of Neeman and Ranicki.Comment: to appear in Advances in Mathematic
Totally asymmetric exclusion process with long-range hopping
Generalization of the one-dimensional totally asymmetric exclusion process
(TASEP) with open boundary conditions in which particles are allowed to jump
sites ahead with the probability is studied by
Monte Carlo simulations and the domain-wall approach. For the
standard TASEP phase diagram is recovered, but the density profiles near the
transition lines display new features when . At the first-order
transition line, the domain-wall is localized and phase separation is observed.
In the maximum-current phase the profile has an algebraic decay with a
-dependent exponent. Within the regime, where the
transitions are found to be absent, analytical results in the continuum
mean-field approximation are derived in the limit .Comment: 10 pages, 9 figure
Weak Chaos in a Quantum Kepler Problem
Transition from regular to chaotic dynamics in a crystal made of singular
scatterers can be reached by varying either sigma
or lambda. We map the problem to a localization problem, and find that in all
space dimensions the transition occurs at sigma=1, i.e., Coulomb potential has
marginal singularity. We study the critical line sigma=1 by means of a
renormalization group technique, and describe universality classes of this new
transition. An RG equation is written in the basis of states localized in
momentum space. The RG flow evolves the distribution of coupling parameters to
a universal stationary distribution. Analytic properties of the RG equation are
similar to that of Boltzmann kinetic equation: the RG dynamics has integrals of
motion and obeys an H-theorem. The RG results for sigma=1 are used to derive
scaling laws for transport and to calculate critical exponents.Comment: 28 pages, ReVTeX, 4 EPS figures, to appear in the I. M. Lifshitz
memorial volume of Physics Report
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